Notes on the Schur-convexity of the extended mean values
Taiwanese Journal of Mathematics, 2005•projecteuclid.org
In this article, the Schur-convexities of the weighted arithmetic mean of function and the
extended mean values are proved. Moreover, some inequalities involving the arithmetic
mean, the harmonic mean, the logarithmic mean, and comparison between the extended
mean values and the generalized weighted mean with two parameters and constant weight
are obtained.
extended mean values are proved. Moreover, some inequalities involving the arithmetic
mean, the harmonic mean, the logarithmic mean, and comparison between the extended
mean values and the generalized weighted mean with two parameters and constant weight
are obtained.
In this article, the Schur-convexities of the weighted arithmetic mean of function and the extended mean values are proved. Moreover, some inequalities involving the arithmetic mean, the harmonic mean, the logarithmic mean, and comparison between the extended mean values and the generalized weighted mean with two parameters and constant weight are obtained.
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